Transcript Slope-Intercept Form

Objective
The student will be able to:
1) write equations using slope-intercept
form.
2) identify slope and y-intercept from an
equation.
Important!!!
This is one of the big concepts in
Algebra 1. You need to
thoroughly understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept
Writing Equations
When asked to write an
equation, you need to know
two things – slope (m) and yintercept (b).
There are two types of
problems you will face.
Writing Equations – Type #1
Write an equation in slope-intercept form of the line that has a
slope of 2 and a y-intercept of 6.
To write an equation, you need two things:
slope (m) =
2
y – intercept (b) =
6
We have both!! Plug them into slope-intercept form
y = mx + b
y = 2x + 6
Writing Equations – Type #2
Write an equation of the line that has a slope of 3 and goes
through the point (2,1).
To write an equation, you need two things:
slope (m) =
3
y – intercept (b) =
???
We have to find the y-intercept!! Plug in the slope and ordered
pair into
y = mx + b
1 = 3(2) + b
Writing Equations – Type #2
1 = 3(2) + b
Solve the equation for b
1=6+b
-6
-6
-5 =
b
To write an equation, you need two things:
slope (m) =
3
y – intercept (b) =
y = 3x - 5
-5
To find the slope and y-intercept
of an equation, write the
equation in slope-intercept form:
y = mx + b.
Find the slope and y-intercept.
y = 3x – 7
y = mx + b
m = 3, b = -7
Find the slope and yintercept.
1)
y =2 x
3
y = mx + b
2
y= x+0
3
2) y = 5
y = mx + b
y = 0x + 5
2
m=
3
b=0
m=0
b=5
Find the slope and y-intercept.
5x - 3y = 6
Write it in slope-intercept form. (y = mx + b)
5x – 3y = 6
-3y = -5x + 6
-3
-3 -3
y=
5
3
x-2
5
m=
3
b = -2
Find the slope and y-intercept.
2y + 2 = 4x
Write it in slope-intercept form. (y
= mx + b)
m=2
b = -1
2y + 2 = 4x
2y
= 4x - 2
2
2
2
y = 2x - 1
Try These!
Suppose we have a
line with a slope of
-1 and passes
through the point
(3, 4).
Suppose we have a
line with a slope of
2 and passes
through the point
(1, 3).
Write the Equation of a Line from
a Graph
 Where does the
line cross the yaxis?
◦ At the point (0, -4)
◦ The y-intercept is -4.
 What is the slope
of the line?
y = mx + b
y = 2x + (-4)
y = 2x -4
◦ The graph also crosses the
x-axis at (2, 0).
◦ We can use the slope
formula to find our slope.
m = -4 – 0 = -4 = 2
0 – 2 -2
We know our slope is 2 and
our y-intercept is -4, what
is the equation of our line?
Using a graph
 Where does the line
cross the y-axis?
◦ At the point (0, 2)
◦ So the y-intercept b is 2.
 The line also passes
through the point (3, 0).
 We can use these points
to find the slope of the
line. How? What
formula do we use?
◦ Using the slope formula,
we find that the slope m
is -2/3.
◦ Write the equation of the
line.
 y= mx + b
 y = (-2/3)x + 2
Slope-Intercept Form– requires the
y-intercept and the slope of the line.


Slope-Intercept Form:


Slope-Intercept Form:


Solving Problems
The pool Entertainment company learned that by pricing
a pool toy at $10, local sales will reach 200 a week.
Lowering the price to $9 will cause sales to rise to 250 a
week.
a. Assume that the relationship between sales price and
number of toys sold is linear. Write an equation that
describes the relationship in slope-intercept form. Use
ordered pairs of the form (sales price, number sold).
b. Predict the weekly sales of the toy if the price is
$7.50.
Solving Problems
 sales price, number sold 
10, 200 9, 250
250  200
m
9  10
50
m
1
m  50
y  200  50  x 10
y  250  50  x  9
y  200  50 x  500
y  250  50 x  450
y  50 x  700
y  50 x  700
Solving Problems
 sales price, number sold 
Predict the weekly sales of the toy if the price is $7.50.
x  7.50
y  50 x  700
y  50 7.50  700
y  375  700
y  325 items sold